Algebraic structures of MRD codes

DOI10.3934/amc.2016021zbMath1348.94102arXiv1502.02711OpenAlexW2964046759MaRDI QIDQ326329

Michael Kiermaier, Alfred Wassermann, Wolfgang Willems, Javier de la Cruz

Publication date: 12 October 2016

Published in: Advances in Mathematics of Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.02711

zbMATH Keywords

semifieldsnetwork codingMRD codesquasifieldsrank distance

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27)

Related Items (29)

Non-linear maximum rank distance codes in the cyclic model for the field reduction of finite geometries ⋮ A new family of linear maximum rank distance codes ⋮ Construction of subspace codes through linkage ⋮ Explicit constructions of some non-Gabidulin linear maximum rank distance codes ⋮ Hermitian rank distance codes ⋮ Non-minimum tensor rank Gabidulin codes ⋮ On the number of inequivalent Gabidulin codes ⋮ On dually almost MRD codes ⋮ On \(q\)-Steiner systems from rank metric codes ⋮ On kernels and nuclei of rank metric codes ⋮ New criteria for MRD and Gabidulin codes and some rank-metric code constructions ⋮ Automorphism groups and new constructions of maximum additive rank metric codes with restrictions ⋮ Nuclei and automorphism groups of generalized twisted Gabidulin codes ⋮ Identifiers for MRD-codes ⋮ Rank-Metric Codes, Semifields, and the Average Critical Problem ⋮ Weight distribution of rank-metric codes ⋮ New semifields and new MRD codes from skew polynomial rings ⋮ On the genericity of maximum rank distance and Gabidulin codes ⋮ Some new non-additive maximum rank distance codes ⋮ MacWilliams' extension theorem for rank-metric codes ⋮ Classification of large partial plane spreads in \(\mathrm{PG}(6,2)\) and related combinatorial objects ⋮ Classes and equivalence of linear sets in \(\mathrm{PG}(1,q^{n})\) ⋮ Generalized twisted Gabidulin codes ⋮ Partition-balanced families of codes and asymptotic enumeration in coding theory ⋮ Vertex properties of maximum scattered linear sets of \(\mathrm{PG} ( 1 , q^n )\) ⋮ Puncturing maximum rank distance codes ⋮ MRD codes with maximum idealizers ⋮ Binary additive MRD codes with minimum distance \(n-1\) must contain a semifield spread set ⋮ Rank-Metric Codes and Their Applications

Uses Software

• Magma

Cites Work

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